Multidimensional Ultrasound Doppler Signal Analysis

for Fetal Activity Monitoring

Sophie Ribes, Jean-Marc Girault, Franck Perrotin, Denis Kouame

To cite this version:

Sophie Ribes, Jean-Marc Girault, Franck Perrotin, Denis Kouame. Multidimensional Ultra-sound Doppler Signal Analysis for Fetal Activity Monitoring. Ultrasound in Medicine andBiology, Elsevier, 2015, vol. 41 (n 12), pp. 3172-3181. <10.1016/j.ultrasmedbio.2015.07.026>.<hal-01343002>

HAL Id: hal-01343002

https://hal.archives-ouvertes.fr/hal-01343002

Submitted on 7 Jul 2016

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

To link to this article : DOI: 10.1016/j.ultrasmedbio.2015.07.026 URL : http://dx.doi.org/10.1016/j.ultrasmedbio.2015.07.026

To cite this version : Ribes, Sophie and Girault, Jean-Marc and Perrotin, Franck and Kouamé, Denis Multidimensional Ultrasound Doppler Signal Analysis for Fetal Activity Monitoring. (2015) Ultrasound in Medicine and Biology, vol. 41 (n° 12). pp. 3172-3181. ISSN 0301-5629

Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15388

Any correspondence concerning this service should be sent to the repository

administrator: staff-oatao@listes-diff.inp-toulouse.fr

MULTIDIMENSIONAL ULTRASOUND DOPPLER SIGNAL ANALYSIS FOR FETAL

ACTIVITY MONITORING

SOPHIE RIBES,* JEAN-MARC GIRAULT,y FRANCK PERROTIN,z and DENIS KOUAM!E**University of Toulouse III, IRIT UMRCNRS 5505, Toulouse, France; yUniversity of Tours, INSERMU930 Tours, France; and

zCHU Bretonneau, Tours, service de Gynecologie Obst!etrique, INSERM U930, Tours, France

Abstract—Fetal activity parameters such as movements, heart rate and the related parameters are essential indi-cators of fetal wellbeing, and no device provides simultaneous access to and sufficient estimation of all of these pa-rameters to evaluate fetal health. This work was aimed at collecting these parameters to automatically separatehealthy from compromised fetuses. To achieve this goal, we first developed a multi-sensor–multi-gate Doppler sys-tem. Then we recordedmultidimensional Doppler signals and estimated the fetal activity parameters via dedicatedsignal processing techniques. Finally, we combined these parameters into four sets of parameters (or four hyper-parameters) to determine the set of parameters that is able to separate healthy from other fetuses. To validate oursystem, a data set consisting of two groups of fetal signals (normal and compromised) was established and providedby physicians. From the estimated parameters, an instantaneous Manning-like score, referred to as the ultrasonicscore, was calculated and was used together with movements, heart rate and the associated parameters in a clas-sification process employing the support vector machine method. We investigated the influence of the sets of pa-rameters and evaluated the performance of the support vector machine using the computation of sensibility,specificity, percentage of support vectors and total classification error. The sensitivity of the four sets rangedfrom 79% to 100%. Specificity was 100% for all sets. The total classification error ranged from 0% to 20%.The percentage of support vectors ranged from 33% to 49%. Overall, the best results were obtained with theset of parameters consisting of fetal movement, short-term variability, long-term variability, deceleration and ul-trasound score. The sensitivity, specificity, percentage of support vectors and total classification error of this setwere respectively 100%, 100%, 35% and 0%. This indicated our ability to separate the data into two sets (normalfetuses and pathologic fetuses), and the results highlight the excellent match with the clinical classification per-formed by the physicians. This work indicates the feasibility of detecting compromised fetuses and also representsan interesting method of close fetal monitoring during the entire pregnancy. (E-mail: kouame@irit.fr)

Key Words: Fetal monitoring, Fetal heart rhythm, Fetal movement, Multidimensional signals, Support vectormachine.

INTRODUCTION

Fetal monitoring may be required at different times dur-

ing pregnancy to closely monitor certain fetal and

maternal disorders (Manning et al. 1980). Existing

methods, which consist of asking women to count the

number of fetal movements, performing a biophysical

profile or Manning’s test (Manning et al. 1980) or

analyzing general movements, may be either subjective

or time consuming. To automatically monitor fetal activ-

ity, the most commonly used system is the cardiotoco-

gram. This device measures fetal heart rate (FHR) and

uterine contractions (Royal College of Obstetricians

and Gynecologists [RCOG] 2001) but does not provide

any information regarding fetal movements. This may

explain why the performances of major classifiers, which

are based on FHR variability analysis alone (through

different kind of entropies), are on the order of 80% for

specificity and 80% for sensitivity (Ferrario et al.

2006). We believe that additional information may

improve classification performance. There are many

dedicated ultrasound systems that collect additional in-

formation such as fetal movement and pseudo-

breathing. Unfortunately, these systems provide only

partially automated detection of fetal movement

(Karlsonn et al. 2000a) or breathing (Karlsonn et al.

2000b; Yamakoshi et al. 1996).

Some preliminary attempts to overcome these limi-

tations were made by Krib"eche et al. (2007). The main

characteristic of their system is that, because of the large

number of sensors needed to cover an explored area as

large as possible, a large number of Doppler signals

have to be processed. The aim of our work was not to

develop new signal processing methods and evaluate their

performance. Instead, we sought to efficiently combine

some relevant existing signal processing techniques to

achieve the following goals: extract fetal activity features,

such as FHR and movements (and related features), and

efficiently collect these features to differentiate between

normal and potentially compromised fetuses. To achieve

these goals, we needed first to reduce the inherent redun-

dancy related to the large number of acquired Doppler

signals and then to separate fetal from maternal signals

through a blind source separation. The detailed signal

processing algorithms used to extract the fetal activity pa-

rameters are not detailed here. The reader is referred to,

for example, Rouvre et al. (2005), Voicu (2011) and

Voicu et al. (2010, 2014). However, even if the number

of relevant data can be reduced, a fusion step is

required to provide the physical with global

information, for example, an ‘‘ultrasound score,’’ on

which a decision can be based.

Thus, the main challenge of this study, and its incre-

mental value with respect to the previously published

article (Krib"eche et al. 2007), was to develop a method

that enables extraction of the relevant information neces-

sary to construct a global indicator sufficiently pertinent

to classify fetuses into normal and potentially compro-

mised groups. To validate the feasibility, this method

was successfully tested on a heterogeneous data set ob-

tained from pregnant women and composed of FHR,

movement and pseudo-breathing signals. To our knowl-

edge, this automated classification is a new and important

contribution to the search for an objective method for

monitoring fetal activity, which remains an open issue

(Grivell et al. 2010; Kaluzynskia et al. 2011).

This article is arranged as follows:We first described

the device produced by an industrial collaboration and

used for this study, and then briefly introduce the signal

processing techniques used. The ultrasound score is

then introduced and investigated using fetal activity pa-

rameters obtained from real fetal Doppler signals.

Finally, results from classification of sets of fetuses are

discussed.

MATERIALS AND METHODS

Materials

We constructed, in collaboration with Althais Tech-

nologies (Tours, France), a multi-sensor Doppler system

(Surfoetus) that was able to monitor most parts of the fetal

body. Although a complete description of the develop-

ment of this device is beyond the scope of this article,

we briefly provide here a brief description. The system

consists of 12 ultrasound (US) sensors, each with five

gates, working at a frequency of f0 5 2 MHz and an elec-

tronic US device (three electronic pulsed Doppler boards

and one data acquisition board). A low-noise amplifier

amplifies the received signal; a deep compensated ampli-

fier then balances the strong attenuation of the deepest

gates. After complex demodulation and filtering, the

Doppler components are sampled sequentially and con-

verted. Sampling frequency, denoted Fe, is 1 kHz. Five

adjustable gates ranging from 2 to 14 cm are used to

explore the depths. These 12 sensors are divided into

three groups of four sensors, as illustrated in Figure 1.

Group A (US sensors 1–4) is used to explore the fetal tho-

rax, investigating FHR and breathing movements; group

B (sensors 5–8) the upper limbs; and group C (sensors

9–12) the lower limbs. Each sensor is a circular piezo-

electric element 12 mm in diameter. The ultrasound

beam was not focused. A belt was used during recording

to maintain all three groups.

Protocol

In this study, 44 pregnant women at a gestational age

.24 weeks were prospectively enrolled. Inclusion

criteria were singleton pregnancy, absence of significant

maternal complications requiring premature delivery (hy-

pertensive disorders; renal, heart or immunologic pathol-

ogy; pre-existing diabetes), willingness to have

pregnancy followed or delivered locally, maternal age

.18 years and health insurance affiliation. Exclusion

criteria were fetal malformation, maternal significant

complications, pregnancy care in another center and

concomitant participation in another research protocol.

This study was approved by the University’s ethics

committee (Clinical Investigation Centre, Innovation

Fig. 1. Sensor group arrangement. Group A (sensors 1–4) ex-plores the fetal thorax, investigating fetal heart rate and breath-ing movements. Group B (sensors 5–8) explores the upperlimbs, and group C (sensors 9–12), the lower limbs. A belt is

used during recording to prevent sensor movement.

Technology, Ethics). The ethics ID number was 2004-32,

and the study number was CT04-SURFOETUS. All par-

ticipants submitted a signed informed consent.

The standard demographic measures, expressed as

the mean 6 standard deviation (range) were age 5 29.9

6 5.9 (20–44) years, height 5 164 6 6 (151–179) cm

and weight 5 63.23 6 15.88 (41–123) kg. Pregnancies

were classified in two groups: normal and IUGR (intra-

uterine growth restriction) depending on ultrasound-

estimated fetal growth at inclusion. IUGR was defined

as an estimated fetal weight under the 10th percentile

or a transverse abdominal perimeter below the 10th

percentile for gestational age. All recordings were per-

formed between the 24th and 40th weeks of gestation in

the Obstetrics Department of Bretonneau University Hos-

pital, Tours, France. In the ‘‘normal’’ group, recordings

were performed every 4 weeks, and in the ‘‘IUGR’’

group, recordings were performed every 2 weeks. The

overall mean gestational age was 30.2 weeks

(median 5 32 weeks). The mean gestational age of the

normal group was 30.1 weeks, and the mean gestational

age of the IUGR group was 29.9 weeks.

Overall, we obtained 98 Doppler signals for the 44

patients. Each examination in this protocol was 30 min

long. The first group, referred to as ‘‘normal pregnan-

cies,’’ consisted of 74 measurements and 31 subjects.

The second group, referred to as ‘‘pathologic pregnan-

cies’’ or ‘‘group with IUGR’’ consisted of 24 measure-

ments and 13 subjects.

Procedures

Asmentioned earlier, the electronic control system is

composed of 12 sensors with five gates per sensor, and

thus, 60 complex Doppler signals must be processed

each millisecond. This is a very large amount of data

with inevitable redundancy in the signals. Furthermore,

as the signals recorded from different sensors originate

from different sources of signals (fetal heart movement,

maternal heart movement, respiration, etc.), a source sep-

aration is strongly expected to extract fetal signal only.

Assuming that there is an L-dimensional zero-mean signal

source vector sðtÞ5 ½s1ðtÞ;.; sLðtÞ&T, and an M-dimen-

sional data vector xðtÞ5 ½x1ðtÞ;.; xMðtÞ&T observed at

each time point t. In short, L is the number of sources,

and M is the number of observable mixed data. L and M

are generally different. These signals can be modeled as

xðtÞ5A:sðtÞ1uðtÞ (1)

where x represents the signals observed or acquired by the

sensors, referred to below as the ‘‘observation matrix’’; A

is the mixing matrix, corresponding to maternal body

‘‘mixing’’; s is the unobservable source matrix; and u(t)

is a zero-mean Gaussian noise vector with a covariance

matrix L. In summary, we have different source signals

denoted s non-observable, which are mixed and acquired

by the sensors and denoted x. As stated before, the fetal

signals need to be extracted and separated to correctly

monitor fetal activity. To perform an unsupervised source

separation, that is, without any a priori information, the

number of independent sources must be evaluated from

our data set. To do so in a parsimonious way, a redun-

dancy information reduction must be performed.

Dimension reduction and sparse blind source

separation

From the set of data, we perform dimension reduc-

tion to eliminate the data redundancy (see Appendix

A). We searched for the number of independent sources

using the method described in Appendix A. This number

of independent sources was found to be two or three.

Knowing the number of sources, we performed signal

separation to separate the fetal Doppler signal from the

mother’s signal (see Appendix B). The last technique to

be explored concerned the statement of a meta-

descriptor allowing an objective evaluation of fetal state.

Ultrasound score

To compute an objective parameter including infor-

mation on fetal heart rate and fetal movements, we intro-

duced a Manning-like hyper-parameter referred to as the

ultrasound score (Ribes et al. 2011). This meta-descriptor

was computed every minute during each examination, as

explained later. The ultrasound score is the sum of five

values denoted V1, V2, V3, V4 and V5 that are based on

the estimated fetal activity parameters, as reported in

Table 1.

V1 and V2 were both based on the fetal heart rate,

which is an essential component in the follow-up of preg-

nancies (Rouvre et al. 2005; Voicu et al. 2010) because it

is correlated with fetal health. As reported in Table 1, V1

represents the baseline (or mean value of FHR), and V2

represents the variance of the baseline. This baseline is

the mean FHR computed when the variability was bet-

ween 5 and 25 bpm over 1 minute. The baseline is

rounded to increments of 5 bpm during a 10-min segment.

The normal value lies between 110 and 160 bpm. Detec-

tion of the FHR may be improved using a specific prior

(Manning 1977).

Table 1. Ultrasound score: Parameters computed eachminute, associated variables and resulting points

Parameter Variable Points

Baseline V1 1.5 to 2Baseline variance V2 21.5 to 1Upper limb movements V3 0 to 1Lower limb movements V4 0 to 1Offset V5 2

V3 and V4 are both based on limb movements. V3

represents upper limb movements whereas V4 represents

lower limb movements. These movements can be de-

tected either on the separated magnitudes by their sudden

changes or by searching for the increase or decrease in the

overall phase. However, to eliminate false detection

caused by phase noise, detection of fetal movement was

combined with a threshold algorithm (Karlsonn et al.

2000b). In this algorithm a movement was defined by a

magnitude level above the noise threshold with a mini-

mum duration of 0.2 s, followed by a minimum rest dura-

tion of 0.5 s.

Finally, V5 is an offset.

The empirical range of values was chosen on the

following basis:

' If the baseline was.110 or,160 bpm, the value of V1

was set between 1.5 and 2; otherwise V1 was set at 0.

More precisely, let BL denote the baseline. Thus, V1

is defined as V15 0:01ðBL2110Þ11:5 if

110#BL#160;V15 0 otherwise.

' If the baseline variancewas,17.5, then the value ofV2

was set between 0 and 1; if the baseline variance was

.17.5, but ,22.5, then the value of V2 was set be-

tween 21.5 and 1; otherwise, the value of V2 was set

at 21.5. More precisely, let BLV denote the baseline

variance (which is a positive value). Thus V2 is defined

by V25BLV=17:5 if 0#BLV#17:5;V2520:5ðBLV217:5Þ11 if 17:5,BLV#22:5; andV2521:5 if BLV.22:5.

' If two or more upper limb movements were detected,

the value of V3 was set at 1; otherwise V3 was set at

0. If two or more lower limbmovements were detected,

then the value of V4 was set at 1; otherwise the value of

V4 was set to 0.

' To have a positive ultrasound score, we added an offset

through V5 which is set at 2.

The ultrasound score for the complete recording was

the mean of the ultrasound score computed for each min-

ute. Figure 2 illustrates an example of the ultrasound

score. At the top are the mean FHR and the standard de-

viation for each minute. In the middle are the numbers of

movements detected from the upper limbs (blue) and

lower limbs (magenta). At the bottom is the ultrasound

score calculated from the aforementioned parameters.

As the parameters do not have the same importance

in the follow-up of fetal well-being, we investigated

different sets of parameters through four new parameters

referred to as hyper-parameters:

' Hyper-parameter 1 consisted of baseline, fetal move-

ment and ultrasound score.

' Hyper-parameter 2 consisted of baseline, fetal move-

ment, short-term variability and ultrasound score.

' Hyper-parameter 3 consisted of baseline, fetal move-

ment and short-term variability.

' Hyper-parameter 4 consisted of fetal movement, short-

term variability, long-term variability, deceleration and

ultrasound score.

Note that variability is the fluctuation in the FHR,

quantified as the amplitude peak-to-peak trough in beats

per minute. Short-term variability (STV) of FHR is

commonly used in prediction of fetal distress. STV is

the oscillation of the FHR around the baseline in ampli-

tudes of 5 to 25 bpm, measured on time windows of

3.75 s. Long-term variability is the mean value over a

minute (i.e., the difference between the highest and the

lowest values of FHR).

Recall of used support vector machine method

To find the best hyper-parameter, we propose the

use of support vector machine (SVM) classification.

Different classification methods were evaluated (Duda

et al. 2001), and the SVM method (Ferrario et al.

1999; Vapnik 1995) was better able to classify the

current data. To ensure a better understanding, the

principles of SVM classification are provided in

Appendix C. In this study and using SVM principles,

a score optimization problem can be reformulated as a

classification problem. The problem under consideration

was the study of the separability of the data (normal fe-

tuses vs. compromised fetuses), using only estimation of

the hyper-parameters mentioned earlier. We had a clas-

sification problem in which the kernel function, the set

of hyper-parameters, the kernel function features and

the value of the constraint C had to be chosen. The

choice of kernel functions was studied empirically,

and optimal results were achieved using a polynomial

kernel function defined by

Kðx; x0Þ5 ð11x:x0Þd (2)

where d is the degree defined by the user. To obtain the

best results, the SVM was computed using a polynomial

kernel function for different sets of hyper-parameters,

kernel degrees and a constraint C defined by the user.

First, the data was pre-processed to separate the sig-

nals of the mothers from those of the fetuses, and then the

parameters listed in Table 1 were computed. The effec-

tiveness of the SVM classification was evaluated using

the computation of specificity, sensitivity, percentage of

support vectors and total classification accuracy defined

as follows:

' Specificity is the number of true-negative decisions

divided by the number of normal pregnancies.

' Sensitivity is the number of true-positive decisions

divided by the number of abnormal pregnancies.

' Percentage of support vectors is the number of support

vectors divided by the number of pregnancies.

' Classification accuracy is the number of correct deci-

sions divided by the number of pregnancies.

A true-negative decision occurred when the classi-

fier and the physician suggested the absence of positive

detection. A true-positive decision occurred when the

classifier and the physician suggested a positive

Fig. 2. Top: Mean fetal heart rate and mean STVeach minute. Middle: Number of movements of the upper limbs (blue)and lower limbs (purple). Bottom: Ultrasound score calculated according to parameters. FHR5 fetal heart rate; STV5

short-term variability.

detection. As mentioned previously, a binary clinical

classification (normal pregnancies and pregnancies asso-

ciated with IUGR disorders) was performed by

physicians.

RESULTS

We first searched for the best hyper-parameter. For

different kernel degrees d and different constraints C,

we performed the classification process and compared

classification accuracies. Figure 3 illustrates the relation-

ship between total error and constraint for the different

hyper-parameters: for all hyper-parameters, total error

decreased when constraint C increased. Hyper-

parameters 2 and 3 differed only by consideration of

the ultrasound score, and hyper-parameter 2, which con-

tained this parameter, always yielded greater accuracy

than hyper-parameter 3, confirming that inclusion of the

ultrasound score facilitated and improved the classifica-

tion process. For all constraint C values, hyper-

parameter 4 always yielded the best results, and we chose

to investigate only this hyper-parameter in the remainder

of our study.

To find the optimal degree of the polynomial kernel

function, we evaluated the performance of the classifica-

tion considering hyper-parameter 4 and increasing

constraint C for different degrees, as illustrated in

Figure 4. Higher degrees offered more general solutions,

with a reduction in the number of support vectors, projec-

ting data into a higher-dimensional space and providing a

lower error rate. At the same time, if we chose to use high

levels of constraint C, we obtained better classification

accuracy. The trade-off between the complexity of the de-

cision region and the training error rate can be monitored

by changing parameter C.

Once the effects of the degree, constraint and set of

hyper-parameters had been studied, the results summa-

rized in Tables 2 and 3 were obtained for a degree value

d 5 15 and a constraint value C 5 9.0 3 105 for all

sets of hyper-parameters. Table 2 outlines the distribution

of normal pregnancies, and Table 3, the distribution of

pregnancies that presented with IUGR disorders. Zones

1–4, revealed by the classifier, corresponded to areas

related to the hyper-planes found, as illustrated in

Figure 5. Zones 1 and 4 are the areas in which the fetuses

were classified without any doubt as normal and compro-

mised, respectively. Zones 2 and 3 provided trends and

were associated with probable normality for zone 2 and

probable compromise for zone 3. It can be seen in

Table 2, for all sets of hyper-parameters, that the normal

pregnancies were found only in zones 1 and 2, that is, in

the zones of normality. In Table 3, for the sets of hyper-

parameters 2 and 4, it can be seen that no pregnancy

was classified in zones 1 and 2; there were no false-

negative decisions. From these two tables, we can

Fig. 3. Comparison of the total error for all hyper-parametersand various constraints for a degree value d 5 15. Hyper-

parameter 4 was always better.

Fig. 4. For various values of constraints and various degrees ofkernel, the total error made for hyper-parameter 4 is evaluated.

High degrees and high constraints provided better results.

Table 2. Distribution of normal pregnancies, polynomialkernel function, degree d 5 15, constraint C 5 9.0 3

105*

Zone

Hyper-parameter

1 2 3 4

1 75.67% 68.91% 64.86% 68.91%2 24.32% 31.08% 35.13% 31.08%3 0 0 0 04 0 0 0 0

* Zones 1–4 were provided by the classifier and corresponded to alocation related to the three hyperplanes. Zones 1 and 4 were the zoneswhere the fetuses were clearly classified as normal fetuses and as fetusespresenting intrauterine growth retardation disorders, respectively. Zones2 and 3 provided trends and were associated with probable normality forzone 2 and probable disorder for zone 3.

conclude that hyper-parameters 1–4 can identify all

normal pregnancies (Table 2), and hyper-parameters 2

and 4 can identify all pregnancies that present with an

IUGR disorder (Table 3).

It should be noted that we were able to identify all

normal pregnancies (Table 2) and all pathologic pregnan-

cies (Table 3), and these were good results concerning the

separability of the data. Table 4 provides the overall re-

sults using evaluation of sensitivity and specificity. It

can be seen that all sets of hyper-parameters, including

the ultrasound score, yielded better results. Sensitivity,

specificity and total error rate were excellent for hyper-

parameters 2 and 4, which confirms the separability of

the data in a high-dimensional space. According to the

percentage of support vectors, we suggest use of hyper-

parameter 4, which used fewer support vectors during

the learning stage. Note also that the specificity and sensi-

tivity values included the support vector.

DISCUSSION AND CONCLUSIONS

We have illustrated in this work that combining

some efficient and dedicated signal processing techniques

for extraction of fetal activity features (fetal heart rhythm,

variabilities, fetal limb, accelerations) can enable close

separation of normal from compromised fetuses. To do

so we introduced an ultrasound score, including the pa-

rameters fetal heart rate value, short-term variability

and numbers of movements of the upper and lower limbs.

We combined this score and other fetal activity parame-

ters to obtain different hyper-parameters. Using these

hyper-parameters and a SVM classification method, we

illustrated the ability of our system to separate data into

two sets, normal pregnancies and pathologic pregnancies,

and obtained excellent matches to clinical classifications

performed by physicians. These are valuable results and

indicate an interesting way forward for home fetal moni-

toring. To our knowledge, this system is unique.

This study had two main limitations that will be

investigated in our future works: binary classification

and limited validation. With respect to binary classifica-

tion, we considered here two groups (normal and

IUGR). Different types of pathologies and subgroups of

pathologies, with different stages, could be valuable in

testing the robustness of our method. As for limited vali-

dation, the study was performed in a single clinical center.

Using data from different clinical centers and performing

classification of new and independent data would also

help to enhance the validity of the methods on a large

scale.

Acknowledgments—This study was supported by the Agence Nationalede la Research (Project ANR-07-TECSAN-023, Surfoetus) and per-formed with CIC-IT 1415, Tours. Wewarmly thank Laurent Colin, Phil-ippe Vince, Fabrice Gens and Thierry Pottier from Althias Universityof Tours, Tours, France; Catherine Roussel and Morgane Fournier-Massignan from CHU Bretonneau Tours, France; and Dr. Iulian Voicu.

REFERENCES

Attias H. Independent factor analysis. Neural Comput 1999;11:803–851.

Bingham E, Hyvarinen A. A fast fixed-point algorithm for independentcomponent analysis of complex valued signals. Int J Neural Syst2000;10:1–8.

Table 3. Distribution of the pregnancies presenting withdisorders, polynomial kernel function, degree d 5 15,

constraint C 5 9.0 3 105*

Zone

Hyper-parameter

1 2 3 4

1 4.16% 0 8.33% 02 4.16% 0 12.5% 03 50% 58.33% 70.83% 504 41.66% 41.66% 8.33% 50

* Zones 1–4 were provided by the classifier and corresponded to loca-tion related to the three hyperplanes. Zones 1 and 4 were the zones wherethe fetuses were clearly classified as normal fetuses and as fetuses pre-senting with intrauterine growth retardation disorders, respectively.Zones 2 and 3 provided trends and were associated with probablenormality for zone 2 and probable pathology for zone 3.

Fig. 5. Support vector machine classification. Zones 1–4 areprovided by the classifier and correspond to areas related tothe hyperplanes. Zones 1 and 4 are the areas where the fetuseswere classified respectively as normal fetuses and as abnormalfetuses. Zones 2 and 3 provide respectively trends of probable

normality and probable disorder.

Table 4. Overall evaluation: the total error, thepercentage of support vectors, the sensitivity and thespecificity were computed for all hyper-parameters

Hyper-parameter

1 2 3 4

Total error 20.4% 0 5.1% 0Support vectors 32.65% 37.75% 48.97% 35.71%Sensitivity 91.66% 100% 79.16% 100%Specificity 100% 100% 100% 100%

Cardoso JF. Blind signal separation: Statistical principles. Proc IEEE1998;9:2009–2025.

Cardoso JF. Higher-order contrasts for independent component analysis.Neural Comput 1999;11:157–192.

Davis M, Mitinoudis N. A simple mixture for sparse overcomplete ICA.IEE Proc Vision Image Signal Process 2004;151:35–43.

Duda R, Hart P, Stork D. Pattern classification. 2nd ed. New York: Wi-ley; 2001.

Ferrario M, Signorini MG, Magenes G, Cerutti S. Support-vector net-works. Mach Learn 1999;20:273–297.

Ferrario M, Signorini MG, Magenes G, Cerutti S. Comparison ofentropy-based regularity estimators: Application to the fetal heartrate signal for the identification of fetal distress. IEEE Trans BiomedEng 2006;53:119–125.

Grivell R, Alfirevic Z, Gyte G, Devane D. Antenatal cardiotocographyfor fetal assessment (review). Cochrane Database Syst Rev 2010;1:CD007863.

Ikeda S, Toyama K. Independent component analysis for noisy data:MEG data analysis. Neural Netw 2000;13:1063–1074.

Kaluzynskia K, Kreta T, Czajkowskib K, Sienkob J, Zmigrodzkia J. Sys-tem for objective assessment of fetal activity. Med Eng Phys 2011;33:692–699.

Karlsonn B, Berson M, Helgason T, Geirsson R, Pourcelot L. Effect offetal and maternal breathing on the ultrasonic Doppler signal due tofetal heart movement. Eur J Ultrasound 2000a;11:47–52.

Karlsonn B, Foulqui"ere K, Kaluzynski K, Tranquart F, Fignon A,Pourcelot D, Pourcelot L, Berson M. The Dopfet system: A new ul-trasonic Doppler system for monitoring and characterisation of fetalmovement. Ultrasound Med Biol 2000b;26:1117–1124.

Krib"eche A, Tranquartlow F, KouameD, Pourcelot L. The Actifetus sys-tem: A multidoppler sensor system for monitoring fetal movements.Ultrasound Med Biol 2007;33:430–438.

Lee TW. Independent component analysis: Theory and applications.Norwell, MA: Kluwer Academic; 1998.

Mallat S. A wavelet tour of signal processing. Orlando, FL: AcademicPress; 1998.

Manning F. Fetal breathing movement as a reflexion of fetal status. Post-grad Med 1977;61:116–122.

ManningF, Platt L, Sipos L.Antepartum fetal evaluation:Development ofa fetal biophysical profile. Am J Obstet Genicol 1980;136:787–795.

Ribes S, Kouam!e D, Voicu I, Fournier-Massignan M, Perrotin F,Tranquart F. Support vector machines based multidimensional sig-nals classification for fetal activity characterization. SPIE Med Im-aging 2011;7968:79680D.

Rouvre D, Kouam!e D, Tranquart F, Pourcelot L. Empirical modedecomposition (EMD) for multi-gate, multi-transducer ultrasoundDoppler fetal heart monitoring. In: Proceedings, Fifth IEEE Interna-tional Symposium on Signal Processing and Information Technol-ogy. New York: IEEE; 2005. p. 208–212.

Royal College of Obstetricians and Gynaecologists (RCOG). The use ofelectronic fetalmonitoring: The use and interpretation of cardiotocog-raphy in intrapartum fetal surveillance. London: RCOG Press; 2001.

Touretzky DS, Mozer MC, Hasselmo ME, (eds). Advances in neural in-formation processing systems, Vol 8. Cambridge, MA: MIT Press;1996. p. 145–151.

Vapnik V. The nature of statistical learning theory. Berlin/Heidelberg:Springer-Verlag; 1995.

Voicu I, Girault J, Fournier-Massignan M, Kouam!e D. Robust estima-tion of fetal heart rate form US Doppler signals. Phys Proc 2010;3:691–699.

Voicu I. Analysis, characterization and classification of fetal signals.PhD thesis; 2011 [In French].

Voicu I, M!enigot S, Kouam!e D, Girault J. New estimators and guidelinesfor better use of fetal heart rate estimators with Doppler ultrasounddevices. Comput Math Methods Med 2014;784862.

Yamakoshi Y, Shimizu T, Shinozuka N, Masuda H. Automated fetalbreathing movement detection from internal small displacementmeasurement. Biomed Tech 1996;41:242–247.

APPENDIX A

DIMENSION REDUCTION

We investigated different methods of estimating the number ofsources in an observation matrix such as the maximum descriptionlength, Bayesian information criterion and Akaike information criterion(AIC), which was the most suited to our data set (see also Ikeda andToyama 2000). For convenience, model (1) can be rewritten in theframework of factor analysis as

x5Bf1m1ε (A.1)

where f is normally distributed as f ) Nð0; ImÞ and Im is the m3m iden-tity matrix; ε is normally distributed as ε ) Nð0;SÞ; and S is a diagonalmatrix L3L. f and ε are mutually independent. Signals are analyzed inshort stationary windows, and therefore, because of the stationarity ofε, m and f, for convenience in eqn (A.1) we voluntarily ignore the timevariable t. The mean of x is given by m, which is assumed here to bezero. The optimum number of sources is then estimated using the AIC.

! bB; bS#MLE

5 argmax$$$B;S

LðB;SÞ (A.2)

where Cx is the covariance matrix of x and

LðB;SÞ521

2

ntr&CxðS1BBTÞ21

'1logðdetðS1BBT ÞÞ

1L logð2pÞo

For a set of data xðt5 1;/;NÞ, the AIC is then defined as

AIC52L! bB; bS

#12

N

)Lðm11Þ2mðm21Þ

2

*(A.3)

where

m#Q51

2

n2L112

ffiffiffiffiffiffiffiffiffiffiffiffi8L11

p o(A.4)

To estimate the number of sources in the mixture x, we first esti-mated B and S for 1#m#Q, m being defined by eqn (A.4). The correctnumber of sources m was the one that minimized the AIC. The correctnumber of sources is important a priori information to perform sourceseparation which gives the dimensions of the mixing matrix A to beevaluated.

Once the redundancy was reduced, the next important step was toseparate the different sources in an unsupervised manner.

APPENDIX B

SPARSE BLIND SOURCE SEPARATION

Independent component analysis (ICA) is one of the best knowntechniques used for blind source separation. It aims at recovering unob-served sources from an available mixture observed by sensors. In otherwords, ICA makes it possible to separate independent data from a set ofobservable data. Many algorithms have been developed to perform ICA(e.g., Maxkurt [Cardoso 1999], JADE [Cardoso 1999], Infomax[Touretzky et al. 1996], fastica [Bingham and Hyvarinen 2000;Cardoso 1998; Lee 1998]).

Independent component analysis finds a linear coordinate system(the unmixing system) such that the resulting signals are statistically in-dependent. Derived from (1) and not taking noise into account (i.e.,uðtÞ5 0) is the ICA model

xðtÞ5A:sðtÞ (A.5)

where A is an M3L scalar mixing matrix, in which M is the number ofobservations and L is the number of sources recovered. The goal of ICA

is to find a linear transformation W of the observed matrix x that makesthe output as independent as possible:

zðtÞ5W :xðtÞ5W:A:sðtÞ (A.6)

where z is an estimate of the sources. The sources are recovered whenWis the exact inverse of A up to a permutation, sign and scale change.These methods work well when the noise level is low (typically asignal-to-noise ratio.20 dB); their advantage is that they are the fastesttechniques. However, because of the presence of high noise in our appli-cation, we used techniques including noise in the mixture model. Toreduce ICA drawbacks in terms of noise, Attias (1999) proposed a modelin which the source distributions are a mixture of Gaussians, the param-eters of which are to be estimated jointly with the mixing matrix. More-over, previous studies on ICA and blind source separation assume thatthe source distributions are sparse. Sparsity is the case where the datacan be represented by a very small number of coefficients; that is,most of the source data coefficients are close to zero. Applying a trans-formation such as discrete cosine transform or wavelet transform to theoriginal data can be considered sparse. Sparsity can improve ICA fortwo reasons: first, the statistical accuracy with which the mixing matrixcan be estimated is related to how non-Gaussian the source distributionsare; second, given A, the quality of the source estimates is also better forsparser sources.

Davis and Mitinoudis (2004) proposed a method that assumes thesource distributions to be sparse using Mallat’s modified discrete cosinetransform (Mallat 1998). This technique referred to as sparse blindsource separation uses two Gaussian vectors to model the distributionof source coefficients: one ‘‘on’’ state corresponding to a high-varianceGaussian vector, and one ‘‘off’’ state corresponding to a small variance.It estimates the mixing matrix, the noise covariance and the weights inthe mixture of Gaussians with an expectation maximization–based pro-cedure. Source recovery is performed using the least mean squaremethod.

APPENDIX C

SUPPORT VECTOR MACHINE

CLASSIFICATION

Given the training data set S5 fxi; yig, with xi˛ Rd the trainingvectors and yi 5 f21;11g the associated classes, we used the canonicalform for SVM, which searches for the optimal hyperplane characterizedby a normal w and an offset b that gives the maximum margin and sat-isfies the constraint

yiðw:xi1bÞ$12xi i5 1; 2;. (A.7)

where the xi are a set of positive slack variables, and ‘‘.’’ is the innerproduct. Each vector may be at a distance xi=kwk on the wrong sideof the margin hyperplane. The xi are a measure of the misclassificationerror, and the penalty function is then given by

CXn

i5 1

xi (A.8)

where C is a parameter chosen by the user. A larger C corresponds to ahigher penalty for errors. It is a convex optimization problem, the aim ofwhich is to find the global minimum. Through reformulation of the prob-lem using the Lagrangian multiplier method, the solution is given by thesaddle point of the Lagrange function

Lp 51

2k wk21C

Xn

i5 1

xi2Xn

i5 1

aiðyiðw:xi1bÞ211xiÞ2Xn

i5 1

bixi

(A.9)

where the ðai; biÞ terms are a set of non-negative Lagrangianmultipliers.The minimum of the Lagrangian function is computed with respect to wand b. By setting the respective derivative and substituting these solu-tions, we obtain the dual objective function:

LD 521

2

Xn

i5 1

Xn

j5 1

aiajyiyjxi:xj1Xn

i5 1

ai (A.10)

The minimum solution of the primal problem can be obtained bymaximizing the dual objective function:

~a5 argmaxa

21

2

X

i5 1

n X

j5 1

n

aiajyiyjxi:xj1X

i5 1

n

ai

!

(A.11)

s:t: C$ai$0ci andXn

i5 1

aiyi 5 0 (A.12)

The support vectors are the data points denoted xsfor whichyiðw:x1bÞ211xi 5 0 and ais0. They lie at a distance xi=kwk on thewrong side of the margin hyperplane or on the margin hyperplanes de-noted h1, h2 if xi 5 0. The optimal solution for the normal vector w isexclusively defined by the set of support vectors, and it can be writtenas a linear combination of these support vectors:

~w5

Xn

i5 1

~aiyixi (A.13)

The optimal solution for the offset b can be obtained with

~b5 ys2Xn

i5 1

~aiyiðxi:xsÞ (A.14)

The optimal separating hyperplane is then given by

hðxÞ 5 sign!~w:x1~b

#(A.15)

where sign(.) is the sign function. The optimal linear boundary withthe largest margin in the input space can be found using a restrictednumber of points called support vectors, which guarantee sufficientgeneralization power and robust behavior. In the case where a linearboundary in the input space is ineffective, the original space can bemapped into a high-dimensional space using a non-linear function,and the problem can be solved in this enlarged space. The mappingprocess is based on the chosen kernel K function satisfying Mercer’scondition that

K!xi; xj

#5FðxiÞ:F

!xj#

(A.16)

The input vectors appear only in the form of dot products in eqn(A.11), and by use of the kernel function in eqn (A.16), the optimizationproblem becomes

~a5 argmaxa

21

2

Xn

i5 1

Xn

j5 1

aiajyiyjK!xi; xj

#1

Xn

i5 1

ai

!(A.17)

such that eqn (A.12) is true. The optimal separating hyperplane isthen given by

hðxÞ5 sign

Xn

i5 1

yiaiK!xi; xj

#1b

!

(A.18)

The more general case (where a linear boundary in the inputspace is inappropriate using a mapping function) can be solved. Itcan be shown that a SVM is able to exploit very high dimensionalspace with strong generalization guarantees derived from the max-margin property.